Ross Douthat goes over what he sees as the good and the bad in the Republican tax plans in his column today. He notes the ending of the mandate that people buy health care insurance in the Senate version of the bill and then says:
"In the long run any universal health insurance system will be on a firmer political footing if it finds a way to work without requiring people to buy a product they don’t want."
A "universal" system does mean that everyone has to have health insurance even if they don't want it. It is possible to effectively make people "buy" insurance through the back door if it is paid for with tax revenue. In this case, people pay for their premiums through their taxes, but they don't directly "buy" insurance.
It's possible that Douthat is arguing for some Medicare for All type system, but it's also possible that he doesn't really want a universal health care system.
Thanks to Robert Salzberg for calling this to my attention.